Mathematical modeling of predictive grinding for ball mill

The aim of this work is to design a mathematical model for deriving acoustic signatures by analyzing the sound of a ball mill in its load varying conditions. The paper establishes an appropriate mathematical background that helps to predict dynamic breakage characteristics with respect to particle size distribution of different types of material. Condenser based stereophonic microphones have been used for capturing the acoustic signal with different raw materials at different running conditions of the mill like with load, without load and saved in appropriate format for analysis. Using Kernel Density Estimator, a unique pattern for each state of the running mill is derived, i.e. Gaussian in nature. As a next step we apply Gaussian curve fitting for simulating the patterns based on the statistical parameters. Finally, a mathematical model has been established to follow the crushing operation of the grinding mill in predictive manner. The parameters are tuned in order to minimize the error between the experimental and the simulated results. The model has been validated in real time environment.